Multi-carrier modulation can result in a high peak-to-average power ratio (PAPR) of the transmitted signals. The PAPR is defined as the ratio of a signal's peak power level to its average power level. In the case of conventional OFDM modulation, the amplitude of the transmission is characterized by a substantially Gaussian-shaped probability distribution function. This Gaussian distribution indicates the possibility that some time-domain samples of the transmission may have amplitudes that are very high compared to the average sample amplitude. The resulting PAPR is much higher for conventional multi-carrier signals than for single-carrier signals. This is due to the probability of substantially constructive interference between the carriers.
The high PAPR for conventional multi-carrier signals imposes significant constraints on the transmission circuitry, and can greatly complicate the analog circuitry required for high-fidelity transmission. For example, a high PAPR translates into a large dynamic range at the inputs of digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), necessitating a large number of bits for resolution. This can significantly increase a receiver's cost and complexity. Highly complex filters and amplifiers must be employed to handle high PAPR and the increased resolution. Furthermore, high PAPR results in higher power consumption in the transceiver circuits, further increasing the cost of the circuits and systems used in the analog front end.
Many prior-art techniques adapted to control the PAPR of multi-carrier transmissions employ clipping to attenuate signal amplitudes that exceed a selected threshold. This results in signal loss and an increase in the bit-error rate (BER). Clipping effectively introduces a cancellation impulse signal in the time-domain signal. As known in the art, a time-domain impulse corresponds to additive noise across all subchannels in the frequency domain. Thus clipping effectively reduces the signal-to-noise ratio for all subchannels in the modulated signal. This is not the case for a CI signal. Rather, an impulse constructed from user-allocated subcarriers can be applied to the particular CI phase-space(s) of interest without affecting other CI signal phase spaces. This approach either localizes signal degradation (which is an insignificant problem when channel coding is employed over multiple phase spaces) or slightly reduces bandwidth efficiency, such as by requiring additional information to be sent to the receiver to compensate for PAPR-mitigating signal distortions.
A variety of PAPR-reduction methods are disclosed in U.S. Pat. Nos. 5,623,513, 5,787,113, 5,768,318, and 5,835,536.
Various approaches have been developed to minimize the number of samples that require clipping. According to one class of techniques, data symbols are coded so that the resulting code words reside in a set of transmission symbols that reside below a predetermined PAPR threshold. These techniques reduce bandwidth efficiency due to the resulting coding overhead.
Another well-known approach applies a phase rotation to some of the subchannels to reduce the probability that a predetermined PAPR threshold is exceeded. Assuming a low probability that the original signal exceeds the PAPR threshold, the probability that both the original signal and the transformed signal exceed the threshold is approximately the square of the low probability. This is a particularly useful technique that can be applied to CI signaling because CI signals exhibiting high peaks are relatively rare. In a closely related technique, different data sequences (e.g., a cyclic rotation of the data) for a given data block may be generated. The sequence having the lowest PAPR is then selected for transmission. These and related approaches can greatly reduce clipping. However, control-signal overhead is required to inform the receiver of changes to the transmission signal.
Another approach estimates and corrects the effects of clipping at the receiver. An estimate of the clipping error is generated at the receiver and used to reconstruct a frequency domain compensation signal to remove the effects of any clipping.
In another PAPR-reduction technique, a normalizer is employed for determining a maximum-amplitude value from a plurality of data samples, and then dividing each of the data samples by the maximum amplitude value to produce normalized amplitude values. The normalized values may be provided with non-linear amplification for at least a subset of the values.
Another PAPR-reduction technique employs reserved subcarriers to cancel peaks. A bandwidth-efficient method of reducing the PAPR in DMT transmissions is disclosed in Gatherer and Polley, “Controlling clipping probability in DMT transmission”, Proceedings of the Asilomar Conference on Signals, Systems, and Computers, (1997), pp. 578-584, the contents of which are herein incorporated by reference. A similar method of reducing PAPR is disclosed in T. Starr, J. M. Cioffi and P. J. Silverman, “Understanding Digital Subscriber Line Technology”, published by Prentice-Hall, 1999, which is incorporated by reference. A predetermined number of subcarriers are used to inject symbols that reduce the PAPR of a DMT signal, and an iterative algorithm teaches which symbols are injected. However, to reduce the PAPR significantly, up to 20% of the sub-carriers are required to inject the symbols, leaving fewer sub-carriers for carrying information. In addition, this method is complex. It requires iterative minimization of non-linear functions and computation of several fast Fourier transforms.
Each of these PAPR approaches can be used in combination with CI. The benefits of such combinations yield a higher performance budget from which advantageous combinations of PAPR, bandwidth efficiency, spectral roll-off, and BER are achieved. The benefits of low initial PAPR in CI modulation enhance the effectiveness of prior-art PAPR-reduction techniques.